Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #26011223 | C2 | semidirect |
| 5. Q8⋊#13063436 | C2 | semidirect |
| 6. #26011221 | C2 | semidirect |
| 7. Q8⋊C8×C173 | C2 | semidirect |
| 60. Dic346 | M16 | semidirect |
| 76. Q8×C173 | M16 | semidirect |
| 104. C173 | #1491 | semidirect |
| 112. Q8⋊C8 | D173 | semidirect |
| 167. Q8 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D173 | 2 |
| #26011547 | 2 |
| C4×#14583809 | 2 |
| #26011223 | 2 |
| Q8⋊#13063436 | 2 |
| #26011221 | 2 |
| Q8⋊C8×C173 | 2 |
| #1491 | 173 |